Deterimine the convolution sum of sequences x1[n] = (1, 2, 3) and x2[n] = (2, 1, 4).

The convolution of two sequences can be found by using the formula for convolution sum which is given by:

(y[n] = Σ x1[k] * x2[n-k] ) for all k

Here, x1[n] = (1, 2, 3) and x2[n] = (2, 1, 4)

We can calculate the convolution sum for each n:

For n = 0: y[0] = x1[0] * x2[0] = 1 * 2 = 2

For n = 1: y[1] = x1[0] * x2[1] + x1[1] * x2[0] = 1 * 1 + 2 * 2 = 5

For n = 2: y[2] = x1[0] * x2[2] + x1[1] * x2[1] + x1[2] * x2[0] = 1 * 4 + 2 * 1 + 3 * 2 = 14

For n = 3: y[3] = x1[1] * x2[2] + x1[2] * x2[1] = 2 * 4 + 3 * 1 = 11

For n = 4: y[4] = x1[2] * x2[2] = 3 * 4 = 12

So, the convolution sum of sequences x1[n] and x2[n] is y[n] = (2, 5, 14, 11, 12).